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Yesterday’s selloff in the US Equities markets was fairly mild by
some standards. The cash S&P Index was off -2.28% at
the end of the day, while the Russell 2000 cash and the Nasdaq
Composite were down -3.17% and -2.33%, respectively. To put
this move in perspective, considering all trading days since
1/3/2002 (N=2,871), the average return of the S&P cash Index
has been 0.52 basis points (standard deviation = 136 bp).
Yesterday’s close was just above the 4th percentile; there were
122 days with a lower return. Interesting perhaps, but not
all significant. Why, then, did it feel so much worse to
those of us who watch the markets closely?

A simple return fails to capture the prevailing volatility
conditions. A 2% return in a volatile market that swings 5%
a day on average is much different than a 2% return in a quiet
market. This is what our volatility spike measure
is designed to capture: the ability of moves to surprise
us. It does this by expressing each day’s return as a
standard deviation [1] of the past
20 trading days, so it automatically adjusts to and standardizes
for current volatility conditions. We review about five
thousand markets in multiple regions, across all asset classes,
every day, and have learned from experience that any moves that
register +/- 2.5 standard deviations deserve our attention.
Yesterday’s move was a -3.26 standard deviation spike on the Cash
S&P; since 1/3/2000, there have only been 12 days that had
more extreme readings.

One thing we should immediately be concerned with is that this is
an extremely small sample size. In general, too many
“quantitative studies” over-specify the questions they ask, which
is a form of over-optimization. For instance, someone might
look at days before the Fed announcement when the market is above
the 50 period moving average, and below the 200 period, in the
first two quarters of the year, when the TED spread is greater
than X, when the preceding month had a return greater than Y,
etc. ad nauseum. These kinds of “studies” will
typically find less than 10 events over the past 20 years and
will present statistics from those events as if they were
significant. They are not, because the entire research
process is flawed. However, in our case, we have applied
one very simple, robust filter to the data and have simply
discovered that the current market movement is extreme. It
is justifiable to dig deeper, but we must be on guard. It
is dangerous to ascribe too much significance to any conclusions
drawn from a small sample size.

The first question we might ask is how often does the market
close up following a standard deviation spike less than or equal
to yesterday’s close. Table 1 presents this
information. T + 1 is the first day following (in this
case, it today, 6/2/2011, the date this report is published),
etc. Statistics are reported for each of the first 10 days,
the 15th and the 20th following the large spike. (Note that
the information is presented in a simple count format, which is a
more accurate way to represent small samples than
percentages.) Looking at the universe of all trading days
since 1/3/2000, the S&P Cash has closed up on 52.9% of all
trading days. Table 1 shows an extremely strong
bias for an upward close in today’s session. To verify this
bias, we looked at more data (table not included): Using
the history of the S&P Cash Index back to 1986 (N=6,285), we
find that 70% of all trading days following a standard deviation
spike less than -3.26 (N=37) closed up, compared to 53.5% of all
days closing up in that universe. This is a clear
expression of mean reversion, one of the dominant forces in the
equity markets.

Next, we look at summary statistics for returns following the
event day, presented in Table 2. Again, there is a
clear tendency. The market has strongly outperformed
(remember, the baseline daily mean return is only .53bp) for a
few days following large downward standard deviation spikes, but
there seems to be an equally strong tendency for
underperformance 10 to 15 days out as evidenced by the
large negative mean and median returns on those days. In
addition, the returns following these events have been extremely
volatile, with very high IQR’s and standard deviations.
Lastly, note that the risks seem to be decisively skewed to the
downside: this condition has resulted in one 23% selloff in
15 days, compared to the largest rally of 7%.

All returns are in basis points and reference the
event day as T=0. In other words, the return on T + 3
= Day 3 / Day 0 - 1.

Figure 1 presents this information in the format of violin plots,
which may be unfamiliar to some of our readers. Each bar
presents the same data as the rows of Table 2 (i.e. D1 = T + 1 =
the first day following the event) as a standard box plot, with
the addition of a kernel density estimation, that shows the
distribution of the returns. Most importantly, the small
bright dot shows the median return, while the larger gray area
shows the shape of the distribution. Note that the graph
seems to be very “heavy” under the zero line a few days
out. We can see from this that there does seem to be an
outlier that could be affecting the mean, but note that the
median is also pulled lower. There is no guarantee that
this history will repeat, but understanding that history will
help us to better quantify the most likely emerging volatility
environment. This is the first task of any technical
analysis.

Figure 1. Violin
Plots for Returns, Days Following ≤ -3.26 σ Events.

Lastly, we are deeply suspicious of any work done on sample sizes
this small, and suggest that you should be too. It is far
more appropriate to evaluate these events on a case-by-case
basis, and it is possible to do so with such a small
sample. For your reference, here are the 12 days that had
lower standard deviation spike readings than yesterday, with
their accompanying standard deviation spikes. It is
an interesting exercise to examine the market action preceding
and following each of the dates. This can significantly
enhance our intuition around these events: 2/27/2007:
-8.74, 1/4/2000: -5.81, 4/14/2000: -5.12, 9/17/2001: -4.53,
10/19/2007: -4.46, 4/27/2010: -3.77, 1/29/2002: -3.72, 1/28/2011:
-3.72, 3/12/2001: -3.65, 6/6/2008: -3.45, 9/29/2008: -3.36,
4/16/2010: -3.34.

Conclusions:

Yesterday’s move in the US Equity Markets, while probably not
significant based strictly on the magnitude of the close,
is extremely unusual on a volatility-adjusted basis.

Only 12 days have had larger volatility-adjusted losses since
1/3/2000. Though not strictly correct, it may be useful to
think of this measure as a gauge of the “surprise factor” of a
move.

Following events like this, there has been an extremely
strong historical bias for the move to be partially reversed, and
for the market to close up, on the following trading day.

Further out, there has been a bias to underperform, and for
greatly increased volatility.

The risks seem to be skewed to the downside.

We recommend that intermediate term traders tighten stops to
the 1,290 area
on the S&P Cash, or be prepared to hold much lower.
Nimble traders should
be positioned short on yesterday’s close, and should be prepared
to sell into rallies today. Reasonable risk levels for any
shorts are in the neighborhood of 1,370 on front month (June)
Futures. (Note this last level references futures,
not cash.)

We anticipate elevated volatility. Long vol structures, perhaps with a
downward bias, could be appropriate in this
environment. (e.g. backspreads, broken wing flies,
etc.)

Watch Financials closely over the next
several sessions. Even in yesterday’s broad rout, the
sector still managed to underperform handily. This could be
a good market tell over the next 3-4 weeks.

[1] Technical note:
this is a very short time window so large readings on this
tool are not uncommon. Furthermore, we only use
standard deviations as a convenient unit of measure.
Our usage of this measure absolutely does not imply
that we accept any suggestion of normality in return
distributions. The so-called “bell curve” does not
apply in financial markets. This is only a standardized
unit of measure.